equivalent to the structural symmetry of a Möbius strip, with the number of twists controlled by sign changes in the electromagnetic coupling between the meta-atoms,” Zhang says. “We have further demonstrated that metamaterials with different coupling signs exhibit resonance frequencies that depend on the number but not the locations of the twists. This confirms the topological nature of the symmetry.”

Working with metallic resonant meta-atoms configured as coupled split-ring resonators, Zhang and members of his research group assembled three of these meta-atoms into trimers. Through careful design of the electromagnetic couplings between the constituent meta-atoms, these trimers displayed Möbius C3 symmetry — meaning Möbius cyclic symmetry through three rotations of 120 degrees. The Möbius twists result from a change in the signs of the electromagnetic coupling constants between the constituent meta-atoms.